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102 lines
2.0 KiB
102 lines
2.0 KiB
package gocircomprover
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import (
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"bytes"
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"math/big"
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)
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func arrayOfZeroes(n int) []*big.Int {
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var r []*big.Int
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for i := 0; i < n; i++ {
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r = append(r, new(big.Int).SetInt64(0))
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}
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return r
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}
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func fAdd(a, b *big.Int) *big.Int {
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ab := new(big.Int).Add(a, b)
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return new(big.Int).Mod(ab, R)
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}
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func fSub(a, b *big.Int) *big.Int {
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ab := new(big.Int).Sub(a, b)
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return new(big.Int).Mod(ab, R)
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}
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func fMul(a, b *big.Int) *big.Int {
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ab := new(big.Int).Mul(a, b)
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return new(big.Int).Mod(ab, R)
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}
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func fDiv(a, b *big.Int) *big.Int {
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ab := new(big.Int).Mul(a, new(big.Int).ModInverse(b, R))
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return new(big.Int).Mod(ab, R)
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}
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func fNeg(a *big.Int) *big.Int {
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return new(big.Int).Mod(new(big.Int).Neg(a), R)
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}
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func fInv(a *big.Int) *big.Int {
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return new(big.Int).ModInverse(a, R)
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}
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func fExp(base *big.Int, e *big.Int) *big.Int {
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res := big.NewInt(1)
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rem := new(big.Int).Set(e)
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exp := base
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for !bytes.Equal(rem.Bytes(), big.NewInt(int64(0)).Bytes()) {
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// if BigIsOdd(rem) {
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if rem.Bit(0) == 1 { // .Bit(0) returns 1 when is odd
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res = fMul(res, exp)
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}
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exp = fMul(exp, exp)
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rem = new(big.Int).Rsh(rem, 1)
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}
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return res
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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func polynomialSub(a, b []*big.Int) []*big.Int {
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r := arrayOfZeroes(max(len(a), len(b)))
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for i := 0; i < len(a); i++ {
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r[i] = fAdd(r[i], a[i])
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}
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for i := 0; i < len(b); i++ {
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r[i] = fSub(r[i], b[i])
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}
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return r
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}
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func polynomialMul(a, b []*big.Int) []*big.Int {
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r := arrayOfZeroes(len(a) + len(b) - 1)
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for i := 0; i < len(a); i++ {
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for j := 0; j < len(b); j++ {
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r[i+j] = fAdd(r[i+j], fMul(a[i], b[j]))
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}
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}
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return r
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}
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func polynomialDiv(a, b []*big.Int) ([]*big.Int, []*big.Int) {
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// https://en.wikipedia.org/wiki/Division_algorithm
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r := arrayOfZeroes(len(a) - len(b) + 1)
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rem := a
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for len(rem) >= len(b) {
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l := fDiv(rem[len(rem)-1], b[len(b)-1])
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pos := len(rem) - len(b)
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r[pos] = l
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aux := arrayOfZeroes(pos)
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aux1 := append(aux, l)
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aux2 := polynomialSub(rem, polynomialMul(b, aux1))
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rem = aux2[:len(aux2)-1]
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}
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return r, rem
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}
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